Question

prove that (cosec theta - sin theta = cot theta cos theta )

Answer 1

Step-by-step explanation:

$\csc( \alpha ) - \sin( \alpha ) \\ \\ \\ = \frac{1}{ \sin( \alpha ) } - \sin( \alpha ) \\ \\ \\ = \frac{1 - { \sin}^{2} \alpha }{ \sin( \alpha ) } \\ \\ \\ = \frac{ { \cos }^{2} \alpha }{ \sin( \alpha ) } \\ \\ \\ = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \cos( \alpha ) \\ \\ \\ = \cot( \alpha ) \cos(?)$

THANKS

Answer 2

Answer:

Step-by-step explanation:

1)convert cosec theta to   1/sin theta..

2) perform LCM... you get,

1-sin square theta/ sin theta..

3)now we know that 1 - sin square theta is cos theta ...

you get ,

cos square theta / sin theta on LHS side.

simpify RHS . you get cos square theta.